Data Source and Methodology

• Primary definition: Corporate finance texts (e.g., Brealey–Myers–Allen) define MIRR using a finance rate for negative cash flows and a reinvestment rate for positive cash flows. All calculations strictly follow this definition.
• Spreadsheet parity: The implemented method mirrors widely accepted practice consistent with tools labelled “MIRR” across professional platforms. All calculations strictly follow the formulas and data provided by this source.

The Formula Explained

Glossary of Variables

How It Works: A Step-by-Step Example

Inputs: \(r_f=8\%\), \(r_r=12\%\), annual frequency (\(m=1\)). Cash flows: \(-10{,}000\) at \(t=0\); \(3{,}000\) at \(t=1\); \(4{,}000\) at \(t=2\); \(4{,}000\) at \(t=3\); \(3{,}000\) at \(t=4\). Then \(N=4\).

1. \(PV_{-}=10{,}000\) (already at \(t=0\)).
2. \(TV_{+}=3{,}000(1.12)^{3}+4{,}000(1.12)^{2}+4{,}000(1.12)^{1}+3{,}000(1.12)^{0}\approx 16{,}643.5\).
3. \(\mathrm{MIRR}_{\text{period}}=(16{,}643.5/10{,}000)^{1/4}-1\approx 13.2\%\).
4. \(\mathrm{MIRR}_{\text{annual}}=\mathrm{MIRR}_{\text{period}}\) since \(m=1\).

Frequently Asked Questions (FAQ)

What happens if the last period isn’t the last positive cash flow?

The terminal value compounds each positive cash flow forward to the final period \(N\). Ensure your table includes all periods.

Do timing conventions (begin vs end) matter?

Periods are indexed explicitly (0, 1, 2, …). Assign each cash flow to the correct period to reflect its timing.

Can I mix monthly flows with annual rates?

Yes—set frequency to Monthly (12). The tool converts annual finance/reinvestment rates to per-period rates.

Why is my MIRR “—”?

You must have at least one negative and one positive cash flow, and rates must be > −100%.

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i_f = (1+r_f)^{1/m} - 1, \qquad i_r = (1+r_r)^{1/m} - 1

PV_{-} = \sum_{t \in \mathcal{N}} \frac{|C_t|}{(1+i_f)^t}

TV_{+} = \sum_{t \in \mathcal{P}} C_t \,(1+i_r)^{N - t}

\mathrm{MIRR}_{\text{period}} = \left(\frac{TV_{+}}{PV_{-}}\right)^{\tfrac{1}{N}} - 1, \qquad \mathrm{MIRR}_{\text{annual}} = \left(1+\mathrm{MIRR}_{\text{period}}\right)^{m} - 1

Per-period rates from annual rates \(r_f, r_r\) and frequency \(m\): \[ i_f = (1+r_f)^{1/m} - 1, \qquad i_r = (1+r_r)^{1/m} - 1 \] Present value of negative cash flows (discount at \(i_f\)): \[ PV_{-} = \sum_{t \in \mathcal{N}} \frac{|C_t|}{(1+i_f)^t} \] Terminal value of positive cash flows (compound at \(i_r\)): \[ TV_{+} = \sum_{t \in \mathcal{P}} C_t \,(1+i_r)^{N - t} \] MIRR over \(N\) periods: \[ \mathrm{MIRR}_{\text{period}} = \left(\frac{TV_{+}}{PV_{-}}\right)^{\tfrac{1}{N}} - 1, \qquad \mathrm{MIRR}_{\text{annual}} = \left(1+\mathrm{MIRR}_{\text{period}}\right)^{m} - 1 \] Requires at least one negative and one positive cash flow; otherwise MIRR is undefined.